Date of Award

Summer 8-2022

Author's School

McKelvey School of Engineering

Author's Department

Mechanical Engineering & Materials Science

Degree Name

Master of Science (MS)

Degree Type



Current 3-D finite-state wake models are incapable of simulating a maneuver in which the sign of the free-stream velocity changes direction and the rotor enters its own wake -- as might occur in the case of a helicopter which ascends and then descends. It is the purpose of this work to create a 2-D finite-state wake model which is capable of handling changes in free-stream direction as a precursor to development of a 3-D model that can do the same.

The 2-D finite-state model used for reentry modifications is an existing model created by Peters, Johnson, and Karunamoorthy. By the addition of a parameter which changes the sign of the free-stream accordingly, a model capable of handling forward and backward flight is developed and tested.

Upon testing of the model for an oscillatory free-stream which changes direction, it was discovered that the presence of a singularity causes the system to become unstable. This behavior was determined to be due to a Floquet instability which occurs in periodic freestreams that reverse direction.

Several analytical expressions for the motion of a segment of vorticity in the wake are developed and presented as test cases for future work on an oscillatory free-stream. The finite-state model is found to accurately approximate the effect of the wake vorticity on the airfoil airloads, paving the way for future investigations when the airfoil changes directions and enters its own wake.


English (en)


Dr. David Peters

Committee Members

Dr. Swaminathan Karunamoorthy Dr. Mark Jakiela